Express this quotient in scientific notation: ${\frac{3.960\times 10^{2}} {6.0\times 10^{5}}}$
Answer: Start by collecting like terms together. $= {\frac{3.960} {6.0}} \times{\frac{10^{2}} {10^{5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.66 \times 10^{2\,-\,5}$ $= 0.66 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.66$ is the same as $6.60 \div 10$ , or $6.60 \times 10^{-1}$ $ = {6.60 \times 10^{-1}} \times 10^{-3} $ $= 6.60\times 10^{-4}$